The rush of venture funds has led to bidding wars and heightened concerns that the sector is overvalued

When Tony Xu, chief executive of food-delivery company DoorDash Inc., began raising funding late last year, he told investors he expected to raise up to $250 million to support his growing, five-year-old business.

He misjudged the market. SoftBank Group Corp. and Singapore sovereign-wealth fund GIC, both competing to invest heavily in startups, pushed up the size of the fundraising round to $535 million, people familiar with the deal say.